K12n609
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-3 q^7+4 q^6-6 q^5+7 q^4-6 q^3+6 q^2-4 q+3- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+7 t^2-6 t+5-6 t^{-1} +7 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+3 z^4+2 z^2+1 }[/math] |
| Determinant | 41 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +6 z^6 a^{-4} -z^6 a^{-6} -4 z^4 a^{-2} +12 z^4 a^{-4} -5 z^4 a^{-6} -3 z^2 a^{-2} +11 z^2 a^{-4} -7 z^2 a^{-6} +z^2 a^{-8} +4 a^{-4} -4 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +3 z^9 a^{-3} +4 z^9 a^{-5} +z^9 a^{-7} +3 z^8 a^{-2} -3 z^8 a^{-6} +z^7 a^{-1} -13 z^7 a^{-3} -18 z^7 a^{-5} -4 z^7 a^{-7} -14 z^6 a^{-2} -16 z^6 a^{-4} -z^6 a^{-6} +z^6 a^{-8} -4 z^5 a^{-1} +13 z^5 a^{-3} +22 z^5 a^{-5} +5 z^5 a^{-7} +17 z^4 a^{-2} +27 z^4 a^{-4} +9 z^4 a^{-6} -z^4 a^{-8} +3 z^3 a^{-1} -3 z^3 a^{-3} -8 z^3 a^{-5} +2 z^3 a^{-9} -6 z^2 a^{-2} -16 z^2 a^{-4} -11 z^2 a^{-6} +z^2 a^{-10} +z a^{-3} -z a^{-5} -3 z a^{-7} -z a^{-9} +4 a^{-4} +4 a^{-6} + a^{-8} }[/math] |
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